You can stay overseas after getting your PR status, but you will need to obtain a re-entry permit. The re-entry permit comes with a validity of five years. It is highly recommended to stay in Singapore and work locally for the last 2-3 years out of this 5 year period. This way, you can pay income tax and also show your contribution socially and economically. In case you are sent to work abroad by your company, ICA will demand an explanation during the renewal.
Also the re-entry permit may be issued only for a year or two in that case.